You might have tried a service like the now defunct OnLive. ... Steam recently introduced In-Home Streaming, which basically creates a mini-OnLive in your own home with all the same Steam games I played with my eGPU. But… let’s do it over the Internet!

http://lg.io/2015/04/12/run-your-own-high-end-cloud-gaming-service-on-ec2.html

I've tried it and it works great.